Seth J. Teller and Michael E. Hohmeyer

EECS Department, University of California, Berkeley

Technical Report No. UCB/CSD-92-665

, 1992

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-665.pdf

Given four distinct lines in R^3 there exist zero, one, two, or various infinities of lines incident on the given lines. We wish to characterize and compute the set of incident lines in a numerically stable way. We use the Plucker coordinatization of lines to cast this problem as a null-space computation in R^5, and show how the singular value decomposition (SVD) yields a simple, stable characterization of the incident lines. Finally, we enumerate the types of input degeneracies that may arise, and describe the solution set of lines in each case.

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BibTeX citation:

@techreport{Teller:CSD-92-665,
    Author= {Teller, Seth J. and Hohmeyer, Michael E.},
    Title= {Computing the Lines Piercing Four Lines},
    Year= {1992},
    Month= {Jan},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1992/6126.html},
    Number= {UCB/CSD-92-665},
    Abstract= {Given four distinct lines in R^3 there exist zero, one, two, or various infinities of lines incident on the given lines. We wish to characterize and compute the set of incident lines in a numerically stable way. We use the Plucker coordinatization of lines to cast this problem as a null-space computation in R^5, and show how the singular value decomposition (SVD) yields a simple, stable characterization of the incident lines. Finally, we enumerate the types of input degeneracies that may arise, and describe the solution set of lines in each case.},
}

EndNote citation:

%0 Report
%A Teller, Seth J. 
%A Hohmeyer, Michael E. 
%T Computing the Lines Piercing Four Lines
%I EECS Department, University of California, Berkeley
%D 1992
%@ UCB/CSD-92-665
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1992/6126.html
%F Teller:CSD-92-665